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Theorem 19.12 1847
 Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! But sometimes the converse does hold, as in 19.12vv 1898 and r19.12sn 3789. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)
Assertion
Ref Expression
19.12 (xyφyxφ)

Proof of Theorem 19.12
StepHypRef Expression
1 nfa1 1788 . . 3 yyφ
21nfex 1843 . 2 yxyφ
3 sp 1747 . . 3 (yφφ)
43eximi 1576 . 2 (xyφxφ)
52, 4alrimi 1765 1 (xyφyxφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1541 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax12olem2  1928
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